Abstract
We derive the timescale for two initially pure subsystems to become entangled with each other through an arbitrary Hamiltonian that couples them. The entanglement timescale is inversely proportional to the "correlated uncertainty" between the two subsystems, a quantity which we will define and analyze in this paper. Our result is still applicable when one of the subsystems started in an arbitrarily mixed state, thus it generalizes the well-known "decoherence timescale" while coupled to a thermal state.
Highlights
Quantum entanglement is one of the most intriguing properties of quantum mechanics
We will take a step toward a universal result in the dynamics—the entanglement time scale
It is widely believed that the true theory of quantum gravity exists, and the geometry can be described by some wavefunction formalism. It is by-definition possible for the wave-function of particles in quantum field theory (QFT) to become entangled with the geometry
Summary
Quantum entanglement is one of the most intriguing properties of quantum mechanics. From the kinematics alone, one can already derive surprisingly universal results such as the violation of the Bell inequality and the monogamy of entanglement [1]. We will take a step toward a universal result in the dynamics—the entanglement time scale. We will study two subsystems which started in a pure, product state They evolve to become entangled with each other through couplings in the Hamiltonian. We will show that there is a well-defined, universal time scale in this problem This indicates how fast the two subsystems become entangled with each other. The simple and important lesson here is that entanglement between two subsystems are due to the quantum uncertainty of their coupling. It is widely believed that the true theory of quantum gravity exists, and the geometry can be described by some wavefunction formalism It is by-definition possible for the wave-function of particles in QFT to become entangled with the geometry. IV, we will discuss the general implication and future directions to further generalize our result
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